Very true, and a good point. I thought it was a interesting little gotcha about the whole technique though: sometimes you will actually need to go ahead and look at whole diff to be 100% sure.
Indeed. Whenever you drop the sledgehammer, you have the obligation to exhaustively review its effects at least once to be sure there wasn't collateral damage. The beauty of the second-order diff is that, once you do an exhaustive review, you need not do another one just to adjust the sledgehammer.